Supplementary table 1. Empirical (permutation-based) type 1 error of disregarding-family-structure (DFS), 2-Step and FBAT analyses. Significantly inflated (conservative) type I errors are indicated in bold (italic), P≤0.05.

Pedigree / α=0.05 / α=0.01
MAF / h2 / DFS / 2-Step / FBAT / DFS / 2-Step / FBAT
NP
0.1 / 0.3 / 0.058 / 0.029 / 0.06 / 0.013 / 0.009 / 0.015
0.1 / 0.3q / 0.06 / 0.036 / 0.061 / 0.017 / 0.005 / 0.01
0.1 / 0.5 / 0.073 / 0.022 / 0.048 / 0.015 / 0.002 / 0.01
0.5 / 0.3 / 0.063 / 0.039 / 0.052 / 0.02 / 0.005 / 0.012
0.5 / 0.3q / 0.062 / 0.032 / 0.046 / 0.018 / 0.006 / 0.012
0.5 / 0.5 / 0.085 / 0.028 / 0.042 / 0.019 / 0.003 / 0.008
ERF
0.1 / 0.3 / 0.086 / 0.028 / 0.049 / 0.02 / 0.005 / 0.005
0.1 / 0.3q / 0.077 / 0.031 / 0.056 / 0.022 / 0.005 / 0.007
0.1 / 0.5 / 0.108 / 0.023 / 0.053 / 0.023 / 0.003 / 0.011

Supplementary Table 2. Mean percent of difference (95% distribution interval) and correlation (+s.e.m) between the values of χ2 statistics coming from measured genotypes approach and 2-Step, disregarding-family-structure (DFS), QTDT and FBAT analyses at different pedigree structures (NF, ERF) and QTL explaining 1, 2 and 3% of total variance.

2-Step / DFS / QTDT / FBAT
MAF / h2 / Difference / Corr. / Difference / Corr. / Difference / Corr. / Difference / Corr.
NP / qtl0.01
0.1 / 0.3 / -13.5 (-19.8;-7.4) / 99.74+0.02 / 11.9 (-20.7;55) / 98.08+0.12 / -51.2 (-99.4;53.9) / 63.54+1.85 / -44.4 (-99.4;70.1) / 63.51+1.85
0.1 / 0.3q / -13.6 (-19.9;-7.2) / 99.74+0.02 / 9.7 (-24.1;44) / 98.11+0.12 / -51 (-98;56.9) / 64.92+1.79 / -42.8 (-97.7;83.3) / 62.36+1.9
0.1 / 0.5 / -20.5 (-27;-14.8) / 99.74+0.02 / 13.8 (-39.9;80.1) / 95.03+0.3 / -53.6 (-96.9;23.7) / 69.04+1.62 / -40.7 (-95.8;55.6) / 68.65+1.64
0.5 / 0.3 / -13.6 (-19.4;-7.9) / 99.8+0.01 / 11.5 (-21.3;51.8) / 97.91+0.13 / -54.7 (-97.9;39.6) / 64.98+1.79 / -48 (-97.2;63.1) / 65.05+1.79
0.5 / 0.3q / -13.5 (-20.2;-7.8) / 99.77+0.01 / 10.9 (-23.1;49.8) / 97.83+0.13 / -51.9 (-97.9;45.4) / 59.35+2.01 / -45.9 (-98.6;60) / 58.55+2.04
0.5 / 0.5 / -20.4 (-26;-15.2) / 99.75+0.02 / 18.2 (-43.6;84.7) / 94.72+0.32 / -50.1 (-98.1;45.6) / 68.61+1.64 / -36.4 (-97.8;77.2) / 68.96+1.63
NP / qtl0.02
0.1 / 0.3 / -13.7 (-20.6;-8) / 99.55+0.03 / 9.9 (-11.8;35.2) / 98.17+0.11 / -58.7 (-94.2;-2.1) / 63.63+1.85 / -54.8 (-93.1;5.9) / 62.67+1.89
0.1 / 0.3q / -13.9 (-19.9;-7.5) / 99.63+0.02 / 9.8 (-10.3;36.4) / 98.45+0.09 / -59.6 (-93.8;-8.1) / 64.67+1.81 / -56 (-92.9;3.6) / 60.84+1.96
0.1 / 0.5 / -20.6 (-26.8;-15.1) / 99.57+0.03 / 12.7 (-22.1;52.4) / 95.47+0.27 / -59.8 (-90.2;-18.3) / 70.77+1.55 / -50 (-87.1;0.7) / 69.06+1.62
0.5 / 0.3 / -14 (-20.3;-8) / 99.62+0.02 / 10.8 (-9.6;36.8) / 97.97+0.12 / -61 (-93.6;-7) / 66.78+1.72 / -55.2 (-92.5;6.4) / 66.69+1.72
0.5 / 0.3q / -13.9 (-20.2;-7.7) / 99.55+0.03 / 11.1 (-8.7;34.5) / 97.89+0.13 / -61.8 (-93.9;-12.9) / 66.38+1.73 / -58 (-94.2;-3.1) / 64.68+1.8
0.5 / 0.5 / -20.5 (-26.1;-14.8) / 99.58+0.03 / 12.5 (-22.6;50.7) / 94.73+0.32 / -59.3 (-90.8;-12.9) / 69.89+1.58 / -47.6 (-87.4;14) / 69.56+1.6
NP / qtl0.03
0.1 / 0.3 / -14.3 (-21.4;-7.8) / 99.31+0.04 / 10.2 (-4.5;28.5) / 98.33+0.1 / -61.7 (-89.1;-25) / 66.01+1.75 / -59 (-87.7;-21.2) / 64.88+1.8
0.1 / 0.3q / -14.2 (-21.7;-7.6) / 99.3+0.04 / 9.9 (-7.9;31.1) / 98.11+0.11 / -61 (-90.3;-18.3) / 64.41+1.82 / -58.6 (-90.1;-11.8) / 59.88+1.99
0.1 / 0.5 / -20.9 (-27.9;-15.2) / 99.27+0.04 / 12.7 (-15.3;42.3) / 95.36+0.28 / -61 (-87.2;-27.4) / 69.92+1.58 / -53.1 (-83.5;-10.4) / 67.55+1.69
0.5 / 0.3 / -14.3 (-20.4;-8) / 99.45+0.03 / 10 (-5.9;30.3) / 98.21+0.11 / -61.6 (-89.5;-19.9) / 62.5+1.89 / -56.6 (-87.4;-11.7) / 62.4+1.9
0.5 / 0.3q / -14.3 (-21;-7.7) / 99.25+0.05 / 10.6 (-6.2;29.6) / 98.11+0.12 / -62.3 (-90.6;-19.5) / 62.65+1.89 / -59.8 (-90.4;-15) / 60.07+1.99
0.5 / 0.5 / -20.9 (-26.4;-15.3) / 99.41+0.04 / 13.2 (-15;45.1) / 95+0.3 / -61.5 (-88;-26.2) / 70.83+1.54 / -51.2 (-84.4;-5.6) / 68.89+1.63
ERF / qtl0.01
0.1 / 0.3 / -15.4 (-23.7;-9.5) / 99.74+0.05 / 15.5 (-40.5;85) / 94.21+1.04 / -66.2 (-99.7;22.5) / 39.16+8.24 / -65 (-98.7;44.1) / 36.59+8.45
0.1 / 0.5 / -21.7 (-29.9;-15.4) / 99.64+0.07 / 23.1 (-60.1;169.9) / 88.76+1.97 / -61.7 (-99.9;19) / 50.13+7.21 / -59.3 (-99.9;12.4) / 53.14+6.89
0.5 / 0.3 / -16 (-21.3;-9.6) / 99.76+0.04 / 14 (-44.3;95.6) / 91.84+1.45 / -58.7 (-99.6;93.5) / 52.07+7.01 / -55.7 (-99.7;106.9) / 52.29+6.98
0.5 / 0.5 / -22.7 (-29;-16.4) / 99.48+0.1 / 31.7 (-74.1;138.5) / 88+2.1 / -51.8 (-99.9;146.8) / 43.12+7.89 / -34.8 (-99;141.4) / 53.94+6.8
ERF / qtl0.02
0.1 / 0.3 / -15.7 (-22.2;-7.8) / 99.52+0.09 / 12 (-30.5;58.7) / 95.08+0.89 / -66.8 (-97;-8) / 57.99+6.34 / -67.5 (-96.7;4.9) / 52.73+6.93
0.1 / 0.5 / -22.5 (-31.9;-15.4) / 98.98+0.19 / 20.9 (-28.1;87.3) / 82.35+3.01 / -69.3 (-99.6;-19.3) / 58.31+6.31 / -68.1 (-99.2;-16.7) / 54.67+6.72
0.5 / 0.3 / -15.9 (-23;-9.9) / 99.44+0.1 / 9.5 (-27;47.2) / 93.79+1.11 / -70.6 (-97.9;-14.7) / 51.56+7.06 / -69.8 (-98.5;-18.7) / 52.99+6.91
0.5 / 0.5 / -22 (-29;-16.2) / 99.34+0.12 / 15.2 (-42.7;89.8) / 85.1+2.57 / -67.5 (-97.7;-13) / 39.14+8.24 / -64.6 (-98;-15.9) / 42.82+7.92

Supplementary table 3. Power, based on empirical (permutation-based) threshold of significance for the 2-Step and FBAT analyses.

α=0.05 / α=0.01
MAF / h2 / 2-Step / FBAT / 2-Step / FBAT
NP / qtl0.01
0.1 / 0.3 / 0.798 / 0.507 / 0.606 / 0.273
0.1 / 0.3q / 0.832 / 0.509 / 0.603 / 0.285
0.1 / 0.5 / 0.794 / 0.572 / 0.569 / 0.336
0.5 / 0.3 / 0.83 / 0.533 / 0.645 / 0.285
0.5 / 0.3q / 0.832 / 0.497 / 0.592 / 0.25
0.5 / 0.5 / 0.799 / 0.56 / 0.557 / 0.325
NP / qtl0.02
0.1 / 0.3 / 0.991 / 0.803 / 0.934 / 0.603
0.1 / 0.3q / 0.987 / 0.802 / 0.935 / 0.591
0.1 / 0.5 / 0.984 / 0.869 / 0.927 / 0.665
0.5 / 0.3 / 0.988 / 0.805 / 0.942 / 0.619
0.5 / 0.3q / 0.988 / 0.782 / 0.948 / 0.539
0.5 / 0.5 / 0.973 / 0.868 / 0.918 / 0.668
NP / qtl0.03
0.1 / 0.3 / 0.999 / 0.934 / 0.992 / 0.806
0.1 / 0.3q / 0.997 / 0.923 / 0.991 / 0.793
0.1 / 0.5 / 0.999 / 0.956 / 0.986 / 0.863
0.5 / 0.3 / 1.000 / 0.945 / 0.999 / 0.812
0.5 / 0.3q / 1.000 / 0.916 / 0.992 / 0.781
0.5 / 0.5 / 0.999 / 0.959 / 0.989 / 0.857
ERF / qtl0.01
0.1 / 0.3 / 0.78 / 0.32 / 0.6 / 0.14
0.1 / 0.5 / 0.76 / 0.39 / 0.54 / 0.19
0.5 / 0.3 / 0.84 / 0.34 / 0.52 / 0.12
0.5 / 0.5 / 0.69 / 0.29 / 0.47 / 0.11
ERF / qtl0.02
0.1 / 0.3 / 0.96 / 0.54 / 0.89 / 0.3
0.1 / 0.5 / 0.98 / 0.61 / 0.90 / 0.41
0.5 / 0.3 / 0.95 / 0.51 / 0.90 / 0.24
0.5 / 0.5 / 0.99 / 0.69 / 0.90 / 0.42